The Standard Model of Cosmology, the so-called ΛCDM model [1], is afflicted by
several discrepancies with observations that might be calling for new physics. The Hubble tension between the local measurement of H0 by SH0ES and Planck’s CMB-inferred value already reaches the ~5σ C.L. Others attain the 2-3σ C.L., as the tension between the growth of large-scale structures measured with weak lensing and galaxy clustering probes and Planck. Both have been there for already a decade. See the review [2] and references therein for details. The growth rate tension is usually quantified in terms of the parameter σ8, which is the root-mean-square mass fluctuations at a scale of R8=8h-1Mpc, with h=H0/(100km/s/Mpc) the reduced Hubble parameter. It has been recently argued that the use of σ8 might introduce a bias in cosmological analyses of models with a value of H0 quite different from the one preferred by ΛCDM (h~0.67) [3]. This has been proved to be true in the context of early dark energy models [4] and modified theories of gravity [5].
In this thesis the student will quantify the bias introduced by the use of σ8 in fitting analyses of several dynamical dark energy models. This bias could be playing a crucial role in the assessment of the aforesaid cosmological tensions, and could also be of utmost importance to understand their interplay. The student will derive the most relevant cosmological equations at the background and linear perturbation levels for the various models and familiarize with the Einstein-Boltzmann code CLASS [6], the use of Monte Carlo techniques and samplers, and basic concepts of Bayesian statistics [7], This analysis is expected to shed light on the discussion of the cosmological tensions and give rise to a publication in a high-impact journal in the field.